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A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…

Probability · Mathematics 2011-08-05 Samantha Molinaro , Myron Hlynka , Shan Xu

This paper deals with a single-server queue with modulated arrivals, service requirements and service capacity. In our first result, we derive the mean of the total workload assuming generally distributed service requirements and any…

Probability · Mathematics 2016-02-22 H. Thorsdottir , I. M. Verloop

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…

Probability · Mathematics 2021-07-01 Vyacheslav M. Abramov

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service…

Optimization and Control · Mathematics 2022-03-04 Melis Boran , Bahar Cavdar , Tugce Isik

A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by…

Probability · Mathematics 2018-12-21 Dieter Armbruster , Simone Göttlich , Stephan Knapp

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…

Probability · Mathematics 2020-01-10 Yana Belopolskaya , Guodong Pang , Andrey Sarantsev , Yurii Suhov

In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…

Probability · Mathematics 2018-12-07 Abhishek , Rudesindo Núñez Queija , Marko Boon

We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…

Probability · Mathematics 2015-10-06 Junfei Huang , Hanqin Zhang , Jiheng Zhang

The main target of this paper is to present the Markov chain C that, not giving explicitly the queue lengths stationary probabilities, has the necessary information to its determination for open networks of queues with several classes of…

Probability · Mathematics 2021-10-19 Manuel Alberto M. Ferreira

Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…

Computation · Statistics 2017-11-02 Iker Perez , David Hodge , Theodore Kypraios

We consider an M/M/1 queueing model where customers can strategically decide to enter or leave the queue. We characterize the class of queueing regimes such that, for any parameters of the model, the socially efficient behavior is an…

Theoretical Economics · Economics 2024-10-11 Marco Scarsini , Eran Shmaya

We consider a Markovian many server queueing system in which customers are preemptively scheduled according to exogenously assigned priority levels. The priority levels are randomly assigned from a continuous probability measure rather than…

Performance · Computer Science 2017-01-06 Neal Master , Zhengyuan Zhou , Nicholas Bambos

In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…

Machine Learning · Statistics 2025-05-07 Jung-hun Kim , Min-hwan Oh

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…

Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is…

Performance · Computer Science 2026-05-05 Shefali Ramakrishna , Edwin Peng , Ziv Scully

We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of $K$ customers arrive in the finite time interval $[0,T]$, where arrival times of…

Probability · Mathematics 2024-12-10 Kaito Hayashi , Yoshiaki Inoue , Tetsuya Takine

This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…

Probability · Mathematics 2007-12-28 Guodong Pang , Rishi Talreja , Ward Whitt

We consider an extension of the classical machine-repair model, where we assume that the machines, apart from receiving service from the repairman, also serve queues of products. The extended model can be viewed as a layered queueing…

Probability · Mathematics 2014-12-24 J. L. Dorsman , O. J. Boxma , M. Vlasiou

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models. The Markovian models include M/M/$\infty$, M/M/r and M/M/1+M queues with random resetting, in which a continuous-time Markov…

Probability · Mathematics 2025-11-27 Dongzhou Huang , Guodong Pang , Izabella Stuhl , Yuri Suhov

We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…

Probability · Mathematics 2016-04-12 Assia Boumahdaf